Biography
Alexey Cheskidov obtained his Ph.D. in Mathematics at Indiana University in 2004, and worked at the University of Michigan, the University of Chicago, and the University of Illinois at Chicago between 2004 and 2023, where he was a full Professor starting 2016. He was a member of the Institute for Advanced Study in Princeton in 2021-2022. He joined the Institute for Theoretical Sciences, Westlake University as a Chair Professor of Mathematics in August 2023.
Research
Alexey Cheskidov’s research focuses on some fundamental problems arising in mathematical fluid dynamics and turbulence, including regularity properties of solutions to the Navier-Stokes, Euler, and related equations, dissipation anomaly, Onsager's conjecture, non-uniqueness constructions via convex integration, global attractors, the role of intermittency in turbulent flows.
Representative Publications
1) A. Cheskidov and X. Luo, L^2-critical nonuniqueness for the 2D Navier-Stokes equations, Annals of PDE 9, 13 (2023).
2) A. Cheskidov and X. Luo, Sharp nonuniqueness for the Navier-Stokes equations, Inventiones mathematicae, 229, 987--1054 (2022).
3) A. Cheskidov and R. Shvydkoy, Volumetric theory of intermittency in fully developed turbulence, Archive for Rational Mechanics and Analysis 247, 45 (2023)
4) A. Cheskidov and M. Dai, Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations. Proceedings of the Royal Society of Edinburgh: Section A, 149, 429-446 (2019).
5) A. Cheskidov, M. Dai, and L. Kavlie, Determining modes for the 3D Navier-Stokes equations, Physica D, 374: 1–9 (2018).
6) A. Cheskidov, M. C. Lopes Filho, H. J. Nussenzveig Lopes, and R. Shvydkoy, Energy conservation in two-dimensional incompressible ideal fluids, Communications in Mathematical Physics, 348: 129-143 (2016).
7) A. Cheskidov and R. Shvydkoy, a unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov's dissipation range, J. Math. Fluid Mech., DOI 10.1007 (2014).
8) A. Cheskidov and S. Lu, Uniform global attractors for the nonautonomous 3D Navier-Stokes equations, Advances in Mathematics 267 (2014), 277-306
9) A. Cheskidov and R. Shvydkoy, The regularity of weak solutions of the 3D Navier-Stokes equations in B_ (∞,∞)~(-1), Archive for Rational Mechanics and Analysis, 195, 159-169 (2010).
10) A. Cheskidov, Global attractors of evolutionary systems, J. Dyn. Diff. Equat. 21, 249-268 (2009).
11) A. Cheskidov and S. Friedlander, The vanishing viscosity limit for a dyadic model, Physica D 238, 783-787 (2009).
12) A. Cheskidov, Blow-up in finite time for the dyadic model of the Navier-Stokes equations, AMS Tran., 360, 5101-5120 (2008).
13) A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy, Energy conservation and Onsager's conjecture for the Euler equations, Nonlinearity 21, 1233-1252 (2008).
14) A. Cheskidov and C. Foias, On global attractors of the 3D Navier-Stokes equations, Journal of Differential Equations 231, 714-754 (2006).
15) A. Cheskidov, Boundary layer for the Navier-Stokes-alpha model of fluid turbulence, Archive for Rational Mechanics and Analysis 172, 333-362 (2004).
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